Matrix coefficient identification in an elliptic equation with the convex energy functional method (Q2820676)

The authors consider the matrix coefficient identification in an elliptic equation from measurements with the convex energy functional method. They start with the description of the corresponding direct and inverse problem and introduce a Tikhonov regularization. In order to discretize their problem, they use finite elements with piecewise linear, continuous elements. In addition they introduce the gradient-projection algorithm for the numerical solution for the regularized equation. Based on this, they show the convergence of the numerical method and especially for the discrete regularized solution, where they also provide its error bound. Finally, they present the results of their numerical experiments.